Question

If f(x) = x + 4 and g(x) = 2x - 3, find (g - f)(2).

Write the answer as an integer.

Answer 1

by definition we can write:
\[\left( {g - f} \right)\left( x \right) = g\left( x \right) - f\left( x \right) = \left( {2x - 3} \right) - \left( {x + 4} \right) = ...?\]

Answer 2

okay

Answer 3

hint:
\[\begin{gathered}
\left( {g - f} \right)\left( x \right) = g\left( x \right) - f\left( x \right) = \left( {2x - 3} \right) - \left( {x + 4} \right) = \hfill \\
\hfill \\
= 2x - 3 - x - 4 = ...? \hfill \\
\end{gathered} \]

Answer 4

I got 6

Answer 5

I got a different result

Answer 6

I got 9

Answer 7

hint:
\[\begin{gathered}
\left( {g - f} \right)\left( x \right) = g\left( x \right) - f\left( x \right) = \left( {2x - 3} \right) - \left( {x + 4} \right) = \hfill \\
\hfill \\
= 2x - 3 - x - 4 = x - 7 \hfill \\
\end{gathered} \]

Answer 8

now, replace x with 2, please
what do you get?

Answer 9

-5

Answer 10

that's right!

Answer 11

so would the answer be -5

Answer 12

yes!

Answer 13

If f\left( x \right) = \frac{{2{x^2}}}{{x - 1}}, evaluate for f(-4).

Write only the answer as a decimal or fraction.


also got stuck on this question

Answer 14

is your function, like this:
\[f\left( x \right) = \frac{{2{x^2}}}{{x - 1}}\]

Answer 15

yes

Answer 16

we have to replace x with -4, so we can write:
\[f\left( { - 4} \right) = \frac{{2{{\left( { - 4} \right)}^2}}}{{ - 4 - 1}} = ...?\]

Answer 17

-13

Answer 18

hint:
\[f\left( { - 4} \right) = \frac{{2{{\left( { - 4} \right)}^2}}}{{ - 4 - 1}} = \frac{{2 \times 16}}{{ - 5}} = ...?\]

Answer 19

27

Answer 20

are you sure?
what is 2*16=...?

Answer 21

32

Answer 22

correct! so our answer is:
\[f\left( { - 4} \right) = \frac{{2{{\left( { - 4} \right)}^2}}}{{ - 4 - 1}} = \frac{{2 \times 16}}{{ - 5}} = \frac{{32}}{{ - 5}} = - \frac{{32}}{5}\]

Answer 23

okay